The Pole has never gone beyond the last 16 at Flushing Meadows and had to come from a set and a break down in her last match against Carla Suarez Navarro, while she is also carrying a right shoulder problem.

But she was the more solid player throughout, moving well and frustrating Jankovic, and coming through impressively to win 6-3 7-5.

Radwanska said: "Today was really, really hot and humid and also windy. It was tough. But I came prepared for that. I was practising here before the match and every day was like that.

"I'm trying to use the ice at the first changeover and trying to stay calm and take the shade as well as much as possible. I was feeling like I was melting there.

"I survived the match. In the second set I was just better for a couple of points."

Vinci, who won the WTA Tour title in Dallas last weekend, has her work cut out if she is to make the quarter-finals, though, having lost to Radwanska in all their previous four meetings.

Sixth seed Angelique Kerber continued her impressive run through the draw with a 6-1 6-2 victory over Olga Govortsova of Belarus.

German Kerber, whose meteoric rise up the rankings began with a surprise run to the semi-finals here last year, ousted Venus Williams in a tough three-setter on Thursday night but had no such problems this time.

Govortsova had her blood pressure checked at the end of the first set as she struggled with the heat, but was only kept on court for 56 minutes.

Kerber next faces 10th seed and French Open finalist Sara Errani, who was an even easier 6-1 6-1 winner against Russian qualifier Olga Puchkova.

Ana Ivanovic continued her return to form with an impressive three-set win over American rising star Sloane Stephens in the night session on Arthur Ashe Stadium.

It was a repeat of their clash at the same stage last year, which Ivanovic won, but 19-year-old Stephens has improved a lot and took the opening set on a tie-break.

The 12th seed hit back, though, levelling the match and then pulling away in the decider to win 6-7 (4/7) 6-4 6-2.

In the fourth round Ivanovic will play unseeded Bulgarian Tsvetana Pironkova, a former Wimbledon semi-finalist.